a free gift is distinct from a gift.

Yes, in some societies, including ours, gifts are anything but "free". There is a complicated system of reciprocity to take heed of. Originally, there was nothing in the word gift than meant "without cost to the recipient" or "without the obligation of reciprocity", it is merely an abstract noun based on the verb "to give". It is interesting that the German cognate word Gift means poison, and the Greek word (whence our English dose) had the meaning of a quantity of beneficial drug versus a dose of poison. In the end, a gift is something given.

And, as has been pointed out occasionally on these boards, redundancy is not a bug in language, but a feature.

Ceci n'est pas un seing.